Currently, single fault diagnosis has received mass concern, and the related research achievements are remarkable. However, because of the mutual interaction of subsystems and the coupling of faults characteristics, the diagnosis of multiple intermittent faults commonly existing in industrial systems is still an intractable problem. In order to solve the problem, an improved Constrained Sparse Autoencoder integrated with Correlation Analysis (CA-CSAE) is proposed, further, a diagnosis scheme for multiple intermittent faults is formulated in this paper. The main strategies are as follows. (1) An adaptive loss function and a constraint for initial weight are designed to improve the diversity and accuracy of SAE feature learning. (2) A relational constraint term is constructed to mitigate the effect of data correlation. (3) The evaluation criterion of data correlation degree is put forward to quantify the scope of the method. (4) In order to improve the diagnostic efficiency, ReLU is introduced as the activation function of hidden layer, and L-BFGS algorithm is employed to obtain the optimal solution. (5) Softmax classifier is employed as the output layer to identify fault mode and ensure the reliability of diagnosis results. Finally, comparison experiments and results analysis are conducted to verify the effectiveness and practicability of the proposed method.